"Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character

Richard P. Feynman

Eternally curious, Feynman was always exploring new disciplines and mastering each. In addition to his work in particle physics and mathematics he tackles art (a friend teaches him to draw; he takes a couple of classes; does some work that gets sold; has a one-man exhibit at a major art gallery; then moves on to other interests), learns Spanish before a trip to South America (only to end up in Brazil having to learn Portugese, then getting an invitation to Japan for which he studies Japanese to the point of being somewhat conversant), learns to play the drums (starts by banging on garbage cans at Los Alamos while working on the atomic bomb during WWII; re-visits the pass-time years later after meeting up with a Nigerian street musician; gets discovered by a choreographer in San Francisco and plays for her avant-garde ballet troop which goes on to win international acclaim), takes up locksmithing (fiddling around in high school; breaks into top secret materials at Los Alamos just to prove it can be done) etc.

If you find the following amusing, you'll love the book (and see also The Dilbert Principle). If it's over your head you might still like the book (but see also The Dilbert Principle - you might be management material).

One day at Princeton I was sitting in the lounge and overheard some mathematicians talking about the series for e to the x power which is 1 + x + x²/2! + x³/3!. Each term you get by multiplying the preceding term by x and dividing by the next number. For example, to get the next term after x³/3! You multiply that term by x and divide by 4. It's very simple.

When I was a kid I was excited by series, and had played with this thing. I had computed e using that series, and had seen how quickly the new terms became very small.

I mumbled something about how it was easy to calculate e to any power using that series (you just substitute the power for x).

"Oh yeah?" they said. "Well, the what's e to the 3.3?" said some joker - I think it was Tukey.

I say, "That's easy. It's 27.11."

Tukey knows it isn't so easy to compute all that in your head. "Hey! How'd you do that?"

Another guy says, "You know Feynman, he's just faking it. It's not really right."

They go to get a table, and while they're doing that, I put on a few more figures: "27.1126," I say.

They find it in the table. "It's right! But how'd you do it!"

"I just summed the series."

"Nobody can sum the series that fast. You must just happen to know that one. How about e³?"

"Look," I say. "It's hard work! Only one a day!"

"Hah! It's a fake!" they say, happily.

"All right," I say, "It's 20.085."

They look in the book as I put a few more figures on. They're all excited now, because I got another one right.

Here are these great mathematicians of the day, puzzled at how I can compute e to any power! One of them says, "He just can't be substituting and summing - it's too hard. There's some trick. You couldn't do just any old number like e to the 1.4."

I say, "It's hard work, but for you, OK. It's 4.05."

As they're looking it up, I put on a few more digits and say, "And that's the last one for the day!" and walk out.

What happened was this: I happened to know three numbers - the logarithm of 10 to the base e (needed to convert numbers from base 10 to base e), which is 2.3026 (so I knew that e to the 2.3 is very close to 10), and because of radioactivity (mean-life and half-life), I knew the log of 2 to the base 3, which is .69315 (so I also knew that e to the .7 is nearly equal to 2). I also knew e (to the 1), which is 2.71828.

The first number they gave me was e to the 3.3, which is e to the 2.3 (10) times e, or 27.18. While they were sweating about how I was doing it, I was correcting for the extra .0026 - 2.3026 is a little high.

I knew I couldn't do another one; that was sheer luck. But then the guy said e to the 3: that's e to the 2.3 times e to the .7, or ten times two. So I knew it was 20.something, and while they were worrying how I did it, I adjusted for the .693.

Now I was sure I couldn't do another one, because the last one was again by sheer luck. But the guy said e to the 1.4 which is e to the .7 times itself. So all I had to do is fix up 4 a little bit!

They never did figure out how I did it.

("Surely You're Joking, Mr. Feynman," page 173-4)